Given:
Consider the given expression is:
[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]
By using the quotient property of exponents, we get
[tex]=x^{4-2}y^{-4-(-2)}z^{-2-4}[/tex] [tex]\left[\because \dfrac{a^m}{a^n}=a^{m-n}\right][/tex]
[tex]=x^{2}y^{-4+2}z^{-6}[/tex]
[tex]=x^{2}y^{-2}z^{-6}[/tex]
By using negative exponent property, we get
[tex]=\dfrac{x^{2}}{y^{2}z^{6}}[/tex] [tex]\left[\because a^{-n}=\dfrac{1}{a^n}\right][/tex]
The simplified form of the given expression is [tex]\dfrac{x^{2}}{y^{2}z^{6}}[/tex].
Therefore, the correct option is B.